Diaz's mother, Cilenis Marulanda, and father, Luis Manuel Diaz, were taken by armed men as they were driving in La Guajira province in Northern Colombia on Saturday.
Marulanda was freed within hours and the kidnappers said on Thursday that his father would also be released.
"If he feels right, he will be will us. You can see he didn't sleep a lot," Klopp told a press conference on Friday.
"The news from Colombia gives us a little bit of hope. I cannot say what we will do.
"It's up to him, if he makes himself available or not."
Klopp gave an update on Thiago Alcantara (32), who is not training fully with the first-team squad due to setbacks from the hip injury that has sidelined the midfielder since April.
"Thiago is an ongoing thing. We cannot put any pressure there as well. We expect him to be back at the start of the New Year," Klopp said.
The German said he was unsure when Stefan Bajcetic (19) would return from his injury.
Liverpool are fourth in the table with 23 points, three behind leaders Tottenham Hotspur and one adrift of Arsenal and Manchester City. Luton are 18th with five points.
Klopp said he would not underestimate promoted Luton who have only earned one point in four games at Kenilworth Road this season.
"We will probably face a low block. We will probably face set-pieces with quality, he said.
"All I need is a pitch, an opponent and us there. It's exciting, I love the story."